Solve for $x$ and $y$ using elimination. ${-3x+6y = 12}$ ${3x+5y = 65}$
Solution: We can eliminate $x$ by adding the equations together when the $x$ coefficients have opposite signs. Add the equations together. Notice that the terms $-3x$ and $3x$ cancel out. $11y = 77$ $\dfrac{11y}{{11}} = \dfrac{77}{{11}}$ ${y = 7}$ Now that you know ${y = 7}$ , plug it back into $\thinspace {-3x+6y = 12}\thinspace$ to find $x$ ${-3x + 6}{(7)}{= 12}$ $-3x+42 = 12$ $-3x+42{-42} = 12{-42}$ $-3x = -30$ $\dfrac{-3x}{{-3}} = \dfrac{-30}{{-3}}$ ${x = 10}$ You can also plug ${y = 7}$ into $\thinspace {3x+5y = 65}\thinspace$ and get the same answer for $x$ : ${3x + 5}{(7)}{= 65}$ ${x = 10}$